| _version_ | 1866901542569771008 |
|---|---|
| author | Heydari, Hoshang |
| author_facet | Heydari, Hoshang |
| contents | <p>Symplectic Active Geometrodynamics (SAGD) is developed in this volume as a regulated metric-affine and operator-theoretic framework for non-singular spacetime, spectral geometry, and emergent physical structure. The central object is the global SAGD constraint operator, constructed from metric-curvature, torsional, regulatory, and symplectic sectors. The Gauge-Equivariant Ricci Controller (GERC) provides a geometric regulatory mechanism, while the Metric-to-Torsion Channel Shift (MTCS) redirects high-curvature stress into torsional degrees of freedom. Together, these structures are proposed to stabilize geometric evolution and prevent null-volume singularities.</p> <p>Volume I establishes the foundational architecture of the theory. It begins with an axiomatic and variational formulation of SAGD, including the independent metric-affine structure, torsional sector, symplectic consistency condition, and regulated field equations. It then develops the global constraint equation and the operator formulation of the theory, including the Laplace-type structure, Dirac factorization, heat-kernel representation, spectral flow, semigroup dynamics, and the construction of the physical Hilbert space as the kernel of the SAGD operator.</p> <p>A major focus of the volume is the rigorous operator-theoretic realization of the SAGD framework. Under appropriate ellipticity, coercivity, relative boundedness, compactness, and domain assumptions, the SAGD operator admits a canonical self-adjoint realization, with the Friedrichs construction used where essential self-adjointness is not separately established. The intrinsic Dirac-type operator is introduced through the factorization of the global constraint operator, allowing the physical sector to be characterized equivalently through the Dirac kernel under suitable assumptions.</p> <p>The later chapters develop the spectral and physical consequences of this structure. These include spectral stability, near-kernel dynamics, topological protection, index-theoretic interpretation, heat-kernel geometry, holographic concentration, emergent gauge-like sectors, unitary dynamics inside the physical sector, and the algebra of physical observables. The volume concludes by positioning SAGD as a foundational operator-geometric framework for subsequent volumes on spectral physics, quantum information, measurement theory, and emergent physical phenomena.</p> <p>This work is intended as the foundational volume of a larger SAGD series. Its purpose is to define the mathematical and conceptual backbone of the theory: a regulated geometric dynamics in which spacetime, physical states, spectral observables, and emergent quantum structures are organized by a single global constraint operator and its intrinsic Dirac-geometric realization.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20112481 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Symplectic Active Geometrodynamics Volume I: Foundations, Operator Structure, and Spectral Physics Heydari, Hoshang Symplectic Active Geometrodynamics; SAGD; metric-affine gravity; symplectic geometry; torsion; Gauge-Equivariant Ricci Controller; GERC; Metric-to-Torsion Channel Shift; MTCS; global constraint operator; Dirac factorization; spectral geometry; operator theory; Friedrichs extension; self-adjoint operators; physical Hilbert space; non-singular spacetime; heat-kernel methods; geometric flow; quantum gravity; emergent gauge structure; spectral physics; holography; topological protection <p>Symplectic Active Geometrodynamics (SAGD) is developed in this volume as a regulated metric-affine and operator-theoretic framework for non-singular spacetime, spectral geometry, and emergent physical structure. The central object is the global SAGD constraint operator, constructed from metric-curvature, torsional, regulatory, and symplectic sectors. The Gauge-Equivariant Ricci Controller (GERC) provides a geometric regulatory mechanism, while the Metric-to-Torsion Channel Shift (MTCS) redirects high-curvature stress into torsional degrees of freedom. Together, these structures are proposed to stabilize geometric evolution and prevent null-volume singularities.</p> <p>Volume I establishes the foundational architecture of the theory. It begins with an axiomatic and variational formulation of SAGD, including the independent metric-affine structure, torsional sector, symplectic consistency condition, and regulated field equations. It then develops the global constraint equation and the operator formulation of the theory, including the Laplace-type structure, Dirac factorization, heat-kernel representation, spectral flow, semigroup dynamics, and the construction of the physical Hilbert space as the kernel of the SAGD operator.</p> <p>A major focus of the volume is the rigorous operator-theoretic realization of the SAGD framework. Under appropriate ellipticity, coercivity, relative boundedness, compactness, and domain assumptions, the SAGD operator admits a canonical self-adjoint realization, with the Friedrichs construction used where essential self-adjointness is not separately established. The intrinsic Dirac-type operator is introduced through the factorization of the global constraint operator, allowing the physical sector to be characterized equivalently through the Dirac kernel under suitable assumptions.</p> <p>The later chapters develop the spectral and physical consequences of this structure. These include spectral stability, near-kernel dynamics, topological protection, index-theoretic interpretation, heat-kernel geometry, holographic concentration, emergent gauge-like sectors, unitary dynamics inside the physical sector, and the algebra of physical observables. The volume concludes by positioning SAGD as a foundational operator-geometric framework for subsequent volumes on spectral physics, quantum information, measurement theory, and emergent physical phenomena.</p> <p>This work is intended as the foundational volume of a larger SAGD series. Its purpose is to define the mathematical and conceptual backbone of the theory: a regulated geometric dynamics in which spacetime, physical states, spectral observables, and emergent quantum structures are organized by a single global constraint operator and its intrinsic Dirac-geometric realization.</p> |
| title | Symplectic Active Geometrodynamics Volume I: Foundations, Operator Structure, and Spectral Physics |
| topic | Symplectic Active Geometrodynamics; SAGD; metric-affine gravity; symplectic geometry; torsion; Gauge-Equivariant Ricci Controller; GERC; Metric-to-Torsion Channel Shift; MTCS; global constraint operator; Dirac factorization; spectral geometry; operator theory; Friedrichs extension; self-adjoint operators; physical Hilbert space; non-singular spacetime; heat-kernel methods; geometric flow; quantum gravity; emergent gauge structure; spectral physics; holography; topological protection |
| url | https://doi.org/10.5281/zenodo.20112481 |